288. SAMPLED-DATA CONTROL SYSTEMS 
Referring to Fig. 11.4, the impulsive response b(¢) of a data hold of this 
type is a triangle-shaped function whose apex is at zero, its altitude equal 
to unity, and its base equal to 27. It is clear that this is the impulsive 
response of a physically unrealizable system since an output is produced 
before the application of the impulse att = 0. To find the transfer func- 
B(é) 

(a) 
Fia. 11.4. (a) Impulsive response of generating triangle for polygonal approximation. 
(b) Decomposition of generating triangle into ramp functions. 
tion, the impulsive response is decomposed into three elementary ramp 
functions, as shown in Fig. 11.4b, the sum of which is the triangle of Fig. 
11.4a. The Laplace transform of these three components is 
1 a 1 
Tet aT Age cr a’) 
Combining these terms and simplifying, 
Bg) = eet (11.5) 
Sats? 
The use of the polygonal or “‘triangle”’ hold having the transfer function 
given in (11.5) results in increased accuracy of computation in most cases. 
To illustrate the point, the same illustrative example considered pre- 
viously will be repeated with the triangle hold in place of the simple data 
clamp. 
EXAMPLE 
The transfer functions of the data hold B(s) and the continuous ele- 
ment G,(s) are as follows 
8 —s)\2 
B(s) a é (1 a ) 
tt 
1+és 

and G,(s) = 
